Optimization governed by stochastic partial differential equations

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dc.contributor.advisorHeinkenschloss, Matthiasen_US
dc.creatorKouri, Drew P.en_US
dc.date.accessioned2011-07-25T02:05:08Zen_US
dc.date.available2011-07-25T02:05:08Zen_US
dc.date.issued2010en_US
dc.description.abstractThis thesis provides a rigorous framework for the solution of stochastic elliptic partial differential equation (SPDE) constrained optimization problems. In modeling physical processes with differential equations, much of the input data is uncertain (e.g. measurement errors in the diffusivity coefficients). When uncertainty is present, the governing equations become a family of equations indexed by a stochastic variable. Since solutions of these SPDEs enter the objective function, the objective function usually involves statistical moments. These optimization problems governed by SPDEs are posed as a particular class of optimization problems in Banach spaces. This thesis discusses Monte Carlo, stochastic Galerkin, and stochastic collocation methods for the numerical solution of SPDEs and identifies the stochastic collocation method as particularly useful for the optimization of SPDEs. This thesis extends the stochastic collocation method to the optimization context and explores the decoupling nature of this method for gradient and Hessian computations.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH. SCI. 2010 KOURIen_US
dc.identifier.citationKouri, Drew P.. "Optimization governed by stochastic partial differential equations." (2010) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/62002">https://hdl.handle.net/1911/62002</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/62002en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectApplied mathematicsen_US
dc.subjectMathematicsen_US
dc.titleOptimization governed by stochastic partial differential equationsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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